Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#11715906 |
| Fitting | Q8×C97 ⋊ C8 |
| Sylow | C97 ⋊ Q8⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊#11715906 |
| commutator | C4×C97 | C2×C8 |
| Frattini | C4 | C2×#11715906 |
| Fitting | Q8×C97 | C8 |
| socle | C2×C97 | C22⋊C8 |
| hypercenter | Q8 | #11715906 |
| hypocenter | C97 | Q8⋊C8 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q8 | |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^64,c^b=ce,g^d=g^22,g^f=g^9688 conjugacy classes — view the full character table.
| maximal subgroup of | C2×Q8⋊#11715906, #27158854, #27158855, … |
| maximal normal subgroup of | C2×Q8⋊#11715906, #27158854, #27158855, … |
| maximal quotient of | #27158736, #27158737, #27158744, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1637);